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RISK ANALYSIS ANDMANAGEMENT -
THEORETICAL APPROACHESAND APPLIED CHALLENGES
Krzysztof Jajuga
Department of Financial Investments andInsurance
Wroc aw University of Economics
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1. Some historical remarks
2. Risk analysis and management - state-of-art
3. Theoretical advances - innovations
4. Applied challenges
Plan
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Methods based on the concept of RISK
- Two old seminal contributions:
Bernoulli (1738), Bachelier (1900)
- Classical contributions - milestones and others:
Markowitz (1952), Roy (1952) - portfolio theory
Black, Scholes (1973), Merton (1973) - derivatives
Modigliani, Miller (1958, 1963) - arbitrage concept
Historical remarks
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Most significant changes in last decade
- growth of risk transfer market
- integration of segments of financial market
- integration of banking, insurance and (pure) financial markets
Markets - today
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MOST SIGNIFICANT CHANGE IN LAST DECADE
INNOV AT ION S !!!!
Markets - today
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Innovations
- theory - increasing sophistication and precision
- practice - increasing technology dependence and wide range
- theory is easily verified in the financial market
- practice stimulates theoretical advances
Markets - today
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Merton (1995): Mathematical models of modern finance contain some of
the most beautiful applications of probability and optimization theory.But of course, all that is beautiful in science need not also be practical;
and surely not all that is practical in science is beautiful. Here we have
both. With all their seemingly abstruse mathematical complexity, the
models of finance theory have nevertheless had a direct and significant
influence on finance practice.
Markets - today
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Types of risk
1. Classical
market risk, credit risk, operational risk
2. N ew - strictly financial
systemic risk, E-risk
3. N ew - coming from other areas
energy risk, insurance risk, weather risk, catastrophe risk, bandwith risk
Risk analysis and management - state -of - art
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Risk measurement - Market risk
V olatility measures
standard deviation and other distributional types of measures
Sensitivity measures
duration, ³greeks´, beta
Risk analysis and management - state -of - art
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Risk measurement - Market risk - Downside risk
V alue at Risk - popularity - deserved or undeserved?
Incremental V aR - amount of risk that position is adding to the portfolio
Marginal V aR - sensitivity of V aR to the changes in the portfolio holdings
Risk analysis and management - state -of - art
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Risk measurement - Market risk
V alue at Risk - what is wrong?
- we do not really know how to estimate
- does not provide the information of the size of losses (if V aR is
exceeded)
- is not subadditive: risk of portfolio could be higher than sum of
individual risks
Risk analysis and management - state -of - art
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Risk measurement - Market risk- Downside risk
O ther downside risk measures:
Lower Partial Moment
Xloss (version of Expected Shortfall) - short horizon, abnormal market
Chance of Losing Money (version of aspiration level) - long horizon,
normal market
Worst Case Performance - long horizon, abnormal market
Risk analysis and management - state -of - art
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Risk measurement - Credit risk
Credit risk models should reflect:
- spread risk
- downgrade risk
- default risk
- recovery rate risk
- concentration risk
Risk analysis and management - state -of - art
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Risk measurement - Credit risk
Credit risk models:
- Credit migration approach (CreditMetrics, Credit V aR)
- O ption pricing approach (KM V )
- Actuarial approach (Credit Risk+)
- Reduced form approach
Risk analysis and management - state -of - art
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Risk management methods
- Insurance (classical)
- ALM - Asset and Liability Methods
- ³Home made´ protection - collateral, guarantees, etc.
- Hedging - derivatives
Risk analysis and management - state -of - art
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Regulations
Basle Committee for Banking Supervision
Basle Accords - moving to internal models
Risk analysis and management - state -of - art
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Financial sector standards -examples
G roup of Thirty - Derivatives, Practices and Principles (1993)
Coopers and Lybrand - G enerally Accepted Risk Principles (1996)
G roup of Twelve: Counterparty Risk Managament Policy G roup -
Improving Counterparty Risk Management Practices (1999)
Algorithmics - Mark to Future (2000)
Risk analysis and management - state -of - art
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Financial sector standards - RiskMetrics type approaches (initially
started by JPMorgan)
O ctober 1994 - first edition of RiskMetrics
December 1996 - RiskMetrics Classic (market risk)
April 1997 - CreditMetrics (credit risk)
April 1999 - CorporateMetrics (enterprise market risk)
April 1999 - LongRun (forecasting and scenario generation methods)
Risk analysis and management - state -of - art
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Some common features of modern approaches
Cross-fertilization of methods in different areas
- finance and insurance
- econophysics
- behavioral finance
Risk analysis and management - state -of - art
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Some common features of modern approaches
Application of financial market type methods in corporate finance
- enterprise-wide risk: Cash Flows at Risk, Earnings at Risk, Earnings Per
Share at Risk
- valuation:Real O ptions V aluation
Risk analysis and management - state -of - art
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Some common features of modern approaches
Integrated risk management - tailoring risk management solutions to the
needs of particular institution taking into account correlation of
different types of risk
Alternative Risk Transfer - designed by (re)insurance sector, for example
captives
Risk analysis and management - state -of - art
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Some common features of modern approaches
Risk Adjusted Performance Measurement (RAPM) - risk adjusted return
measures:
- RAR O
C type approaches (e.g. RAR O
RAC)
- Return on V aR (Ro V aR)
Risk analysis and management - state -of - art
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Some common features of modern approaches
Risk Budgeting - allocating an allowable measure of potential loss to
different aspects of the investment process, monitoring whether those
pieces of investment have exceeded their measure, taking corrective
action when a measure is exceeded and using risk measurement
process to evaluate risk adjusted return
Risk analysis and management - state -of - art
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Theory - main drawbacks of classical approaches
- Unrealistic assumption of normal distribution and geometric Brownian
motion
- In many cases not justifiable assumption of complete market
- Unrealistic assumption of stability of models derived using past data or Monte Carlo simulations
Theoretical innovations
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Theory - main drawbacks of classical approaches
- Markets are incomplete
- High liquidity not present in unstable periods
Theoretical innovations
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Some warnings
Finance is not physics
N icely packed and promoted products may contain rubbish!
People always try to make money on overvalued products before the
others discover overvaluation
Model risk - TBD
Theoretical innovations
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More plausible distributions
- stable distributions
- hyperbolic distributions
- mixtures of distributions
Theoretical innovations
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More plausible processes of financial prices
- mean-reverting process
- jump-diffusion process (combination of Wiener and Poisson) stable
distributions
- gamma process
Theoretical innovations
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Theoretical advances -some other models
- non-linear models (full revaluation instead of linear sensitivities)
- scenario analysis
- stress testing (type of scenario analysis)
Theoretical innovations
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Theoretical advances -emphasis on extremes
- tail estimation (Hill, Pickands, etc.)
- Extreme V alue Theory
a) looking for distribution of maximal loss (Frechet?)
b) looking for distribution of excess loss ( G eneralized Pareto?)
Theoretical innovations
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Integration of different types of risk
Different types of risk (e.g. market, credit) not perfectly correlated,
therefore advantages from ³diversification´
Not so much work except for integration of market and credit risk
Applied challenges
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Normal versus extreme risk
Too small capital allocated exposes institution to excessive levels of risk
Too large capital allocated raises costs and reduces profitability
This problem arises also for clearing institutions
Applied challenges
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Normal versus extreme risk
Remedy - calculate two measures of risk:
normal risk measure, extreme risk measure
then switch between two regimes
Problem: detect switching time
Applied challenges
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Normal versus extreme risk
Possible measures:
V alue at Risk - normal risk, Expected Shortfall - extreme risk
Applied challenges
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Model risk
Financial model risk arises from the fact that the effect of the application
of particular model to the activity on the financial market (valuation,
hedging etc.) may be different from the expected effect
Sometimes considered as operational risk
Applied challenges
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Model risk
- inapplicability of modeling
- incorrect model
- incorrect solution
- inappropriate use
- errors in model processing
Applied challenges
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Model risk
Estimation risk
Risk measures are estimated therefore estimation error should be given
V aR = 10 mln USD may really mean:
With the probability of 0.95
the interval [8.5 mln USD; 11.5 mln USD] contains V aR
Applied challenges
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Merton (1997): At times we can lose sight of the ultimate purpose of the
models when their mathematics become too interesting. The
mathematics of financial models can be applied precisely, but the
models are not all precise in their application to the complex real
world. Their accuracy as a useful approximation to that world varies
significantly across time and place. The models should be applied in
practice only tentatively,with careful assessment of their limitations in
each application.
Applied challenges
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Estimation of volatility
V olatility - measure of individual risk
How to estimate?
Historical - drawback: long time series needed, no prevailing model
Implied - drawback: model dependent, market dependent
Estimation risk - measured by vega
Applied challenges
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Estimation of correlation
Correlation - ³heart´ of risk management
Linear correlation may give misleading conclusions
Linear correlation suitable for elliptical distributions
Linear correlation shows weak tail dependence
Applied challenges
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Measuring dependence with copulas
More general measure of dependence
Can extract from multivariate structure:
- univariate ³marginal structure (individual risks)
- dependence structure
Applied challenges
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Practical implementation problems
- intellectual risk (education badly needed)
- data (past, simulated?)
Applied challenges
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Practical implementation problems - Accounting issues
Working G roup for IAS: Draft Standard:
- more fair value accounting (if market prices are unobservable, use
theoretical valuation model)
- remove hedge accounting
Applied challenges
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Other issues - Risk of risk management
Risk management may require risky tools (as derivatives)
G ains from the use of risk management tools should be larger than risks of
implementing these tools
Applied challenges
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Fundamental question to be answered:
How much risk is too much?
Conclusion